Question

A train covers a distance of 300 km at a uniform speed. If the speed of the train is increased by 5 km/hour, it takes 2 hours less in the journey. Find the original speed of the train.

Answer 1

$distance=d=300km$ ...Given

Let the time taken to cover the distance be $t$ and speed be $x$ km/hr.

Speed $=\frac{\text{distance}}{\text{time}}=\frac{300}{t}=x$ .....(1)

At increased speed,

$\Rightarrow$$x+5=\frac{300}{t-2}$ ...(2)

Substituting eq. (1) in eq.(2), we get

$\Rightarrow$$\frac{300}{t}+5=\frac{300}{t-2}$

$\Rightarrow$$(300+5t)(t-2)=300t$

$\Rightarrow$$300t-600+5t^2-10t=300t$

$\Rightarrow$$5t^2-10t-600=0$

$\therefore t^2-2t-120=0$

$\therefore t^2-12t+10t-120=0$

$\therefore t(t-12)+10(t-12)=0$

$\therefore (t-12)(t+10)=0$

$\therefore t=12$ or $t=-10$

$\because t$ cannot be negative, $t=12hrs$

$\therefore$ Original speed $=\frac{300}{12}=25km/hr.$